Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-7x-3y &= -6 \\ -8x-6y &= -6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $1$ $\begin{align*}14x+6y &= 12\\ -8x-6y &= -6\end{align*}$ Add the top and bottom equations. $6x = 6$ Divide both sides by $6$ and reduce as necessary. $x = 1$ Substitute $1$ for $x$ in the top equation. $-7( 1)-3y = -6$ $-7-3y = -6$ $-3y = 1$ $y = -\dfrac{1}{3}$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{3}$.